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Which Numbers are Real?

Michael Henle

Which Numbers are Real? surveys alternative real number systems: systems that generalize and extend the real numbers while staying close to the properties that make the reals central to mathematics. These systems include, for example, multi-dimensional numbers (the complex numbers, the quaternions, and others), systems that include infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). All the systems presented have applications and several are the subject of current mathematical research.

Which Numbers are Real? will be of interest to anyone who likes numbers, but particularly upper-level undergraduates, graduate students, and mathematics teachers at all levels.